*2.5. CA–Markov Scenario Simulation*

The CA–Markov model predicts land-use change by combining the principles of cellular automata (CA), Markov chains, and multiobjective land allocation [64]. It also has the ability to predict and model spatial changes in complex systems over time. The CA–Markov model integrates spatio-temporal factors in a land-use raster map, treats the land-use type represented by each raster as a metacell state, and uses a land-use transfer area matrix and probability matrix to determine the transfer of metacell states and simulate the change in land-use pattern in a certain region in a specific time.

The simulation process for the PLES distribution of the Yellow River Basin in 2025 was as follows:

The spatial overlay analysis of the land-use data was first processed in ArcGIS and imported into IDRISI software; then, the probability matrix of PLES shift in the Yellow River Basin from 2010 to 2015 was calculated using the Markov model. Considering the data of terrain slope, elevation, and road, the MCE module was used to construct the land-use transfer suitability atlas, and the CA–Markov model was applied to simulate and generate the PLES distribution in 2018. Finally, using the PLES classification data in 2018 as the benchmark, the number of CA cycles was set to 7, based on which the CA–Markov model was used to simulate the PLES distribution of the Yellow River Basin in 2025.
